Abstract
This paper employed the use of Laplace transform to obtain solutions of differential equations of the first and second order with given boundary conditions, also the study investigated the pattern of variation exhibited graphically by the various solutions of differential equations at x = 0 to 12. The results in this study revealed that the solutions obtained usually contain exponential functions, while the differential equations with sine and cosine functions has solution that contains exponential and sine function. Furthermore, the differential equations with cosine function has solution that contain sine function only while differential equations that contain a perfect square multiple of f(x) in which the differential equation is equated to zero may have a solution that contain a sine function only. The graphically representation shows different pattern of variation depending on the solutions of the evaluated differential equations.
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